Question

write the equation in slope intercept form for a line that will pass through (0,3) and have a slope of (-8,15)

Answer 1

The equation of line with the slope m in the slope intercept form is :

y = mx + b

Slope can express as :

$\text{ Slope=}\frac{y_2-y_1}{x_2-x_1}$

Substitute the value :

$(x_1,y_1)=(0,3),(x_2,y_2)=(-8,15)$

$\begin{gathered} \text{ Slope=}\frac{y_2-y_1}{x_2-x_1} \\ Sl\text{ope=}\frac{15-3}{-8-0} \\ \text{ slope=}\frac{12}{-8} \\ \text{slope}=\frac{3}{-2} \end{gathered}$

Substitute the value of slope in the equation of line:

$\begin{gathered} y-3=\frac{3}{-2}(x-0) \\ y-3\text{ =-}\frac{3}{2}x \\ y=-\frac{3}{2}x+3 \end{gathered}$

Equation of line in slope intercept form is :

y = -3/2x + 3

Slope = -3/2

Answer : y = -3/2x + 3

Slope = -3/2