Answer:
y=4x-9
Step-by-step explanation:
The equation of a line is typically written in slope-intercept form, which is y=mx+b. Here's what the variables mean:
y=the y-coordinate
m=the slope
x=the x-coordinate
b=the y-intercept (the point on the line that intercepts the y-axis)
The only values that we have to calculate to find the equation are the slope of the line and the y-intercept. Let's start off by finding the slope.
To find the slope of a line, we would need to find 2 points that fall on the line, [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] and plug them into the expression [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. Let's use the points (1, -5) and (3, 3).
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\frac{3-(-5)}{3-1}[/tex]
[tex]=\frac{3+5}{3-1}\\= \frac{8}{2}\\= 4[/tex]
Therefore, the slope of the line is 4.
To find the y-intercept, all we need to do is look at which point the line crosses the y-axis, and that point is -9.
Finally, we plug the slope and the y-axis into the equation y=mx+b as m and b.
y=mx+b
y=4x-9
I hope this helps!
