Suppose the slope intercept from is y = mx + c
Suppose you know the coordinates of some point P = (p,q) where p � 0 so that P is not the y-intercept,
then the equation of the line is (y-q) = m(x-p)
or y = mx + (-mp+q)
It is easy to see that if P were the y-intercept so that p = 0 and q = c, then this equation would become y = mx + (-m*0 + c) or y = mx + c as would be expected.
Yes.
Converting from point-slope to slope-intercept form is helpful when you want to easily identify the y-intercept of a linear equation, making it simpler to graph the line. Slope-intercept form ((y = mx + b)) clearly shows the slope ((m)) and the y-intercept ((b)), facilitating quick analysis and comparisons with other lines. This conversion is particularly useful in applications involving linear models or when analyzing intersections with other lines.
In the case that you are using Slope-Intercept Form, no, you only plot two points: the y-intercept and one other point. If you don't use Slope-Intercept Form, then you have to use three points.
You can't. There are an infinite number of lines that pass through the point (-2, 3).They all have different y-intercepts and different slopes.In order to narrow it down to a single line, you have to give more information.One more point would do it.=======================================================Here's the minimum information needed to define a unique line:-- you name 2 points; I find slope, intercept, and all other points.-- you name one point and one intercept ... 'x' or 'y'; I find slope and all other points.-- you name x-intercept and y-intercept; I find slope and all other points.-- you name one point and the slope; I find intercept and all other points.-- you name one intercept and the slope; I find all other points.
y=mx+b is slope-intercept form y - y1 = m(x - x1) is point-slope form Used in algebra based math. On a graph; m is the slope b is the y-intercept x and y represent points
Yes.
How do you graph the slope and y intercept? The slope tells you the rise and the run. If the slope is ¾, the change in y =3 and the change in x = 4. Plot the y intercept point If the y intercept point is (0, +3), the slope tells you that a second point on the line is up 3 and right 4 to the point (+3 ,+7). You can go up any multiple of 3, and right the same multiple of 4, to find other points. To draw a good straight line, you need 2 points far apart. Let's move from the y-intercept, (0, +3) up 12 (4*3) and right 16 (4*4) to the point (12, 19). Draw a line through the y-intercept and the point (12, 19).
no it is different
Point slope? y=mx+b M being the slope, and b being the y-intercept.
In the case that you are using Slope-Intercept Form, no, you only plot two points: the y-intercept and one other point. If you don't use Slope-Intercept Form, then you have to use three points.
Neither. Changing the y-intercept will simply move the line up or down the y-axis.The "steepness" is all a matter of the slope.Now that we said that, we can think of a situation where changing the y-interceptwould change the slope of the line:That would be where you were given the y-intercept and one other point, and youhave to find the slope, or find the equation, or draw the line.If somebody sneaks in and changes the y-intercept, but leaves the other point rightwhere it is, then the slope of the line changes, (and so does the equation).
Write the equation in slope-intercept form of the line that has a slope of 2 and contains the point (1, 1).
You can't. There are an infinite number of lines that pass through the point (-2, 3).They all have different y-intercepts and different slopes.In order to narrow it down to a single line, you have to give more information.One more point would do it.=======================================================Here's the minimum information needed to define a unique line:-- you name 2 points; I find slope, intercept, and all other points.-- you name one point and one intercept ... 'x' or 'y'; I find slope and all other points.-- you name x-intercept and y-intercept; I find slope and all other points.-- you name one point and the slope; I find intercept and all other points.-- you name one intercept and the slope; I find all other points.
If you're given an existing point and the slope of the line, then yes - the y-intercept depends on the slope.
You use point-slope form to find the equation of a line if you only have a point and a slope or if you are just given two point. Usually you will convert point-slope form to slope-intercept form to make it easier to use.
y=mx+b is slope-intercept form y - y1 = m(x - x1) is point-slope form Used in algebra based math. On a graph; m is the slope b is the y-intercept x and y represent points
The x-intercept is the point where the graph touches the x-axis.