write the equation of the line, in slope - intercept form, that passes through each set of points. 9. (2,3)…

write the equation of the line, in slope - intercept form, that passes through each set of points. 9. (2,3) and (4,7) 10. (-3,3) and (-1,6)

write the equation of the line, in slope - intercept form, that passes through each set of points. 9. (2,3) and (4,7) 10. (-3,3) and (-1,6)

Answer

Explanation:

Step1: Calculate the slope ($m$)

The formula for slope is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For the points $(2,3)$ and $(4,7)$: $m=\frac{7 - 3}{4 - 2}=\frac{4}{2}=2$

Step2: Use the point - slope form to find the equation

The point - slope form is $y - y_1=m(x - x_1)$. Let's use the point $(2,3)$ and $m = 2$. $y - 3=2(x - 2)$ Expand: $y-3=2x - 4$ Add 3 to both sides: $y=2x-1$

Answer:

$y = 2x-1$