A straight line of points going from top left towards bottom right.
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"In curvilinear relationships, the data points increase together up to a certain point (like a positive relationship) and then as one increases, the other decreases (negative relationship) or vice versa." A linear relation is very simple: if one variable goes up, the other goes up (positive correlation) or goes down (negative correlation). A curvilinear relation between variables is non-linear (i.e., that cannot be described by a straight line). Basically, anythig not linear is curvilinear.
Scatter-plot shows correlation between two different variables (one on the y-axis, the other on x-axis). If there is linear correlation, the scatter-points form a straight line from zero (origo) to some direction. The more cloud-like distribution the scatter-plot does have, the less those variables in question have correlation or dependence with each other.
An equation is the same as a function. Identifying a functional relationship from a graph is nearly impossible unless it is trivially simple like a linear relationship.
Most functions are not like linear equations.
A linear equation looks like a straight line, it sometimes does slope, but it is straight.