Question

write a linear equation in point slope form give two points on the line. then convert the equation to slope intercept form. show all steps. (3,4) and (1,8)

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$. Using points $(3,4)$ and $(1,8)$:
$m=\frac{8-4}{1-3}=\frac{4}{-2}=-2$

Step2: Write point-slope form

Use point $(3,4)$ and $m=-2$. Point-slope form is $y-y_1=m(x-x_1)$:
$y-4=-2(x-3)$

Step3: Expand the right side

Distribute $-2$ across the parentheses:
$y-4=-2x+6$

Step4: Isolate $y$ for slope-intercept form

Add 4 to both sides of the equation:
$y=-2x+6+4$

Step5: Simplify the constant terms

Combine the numerical values:
$y=-2x+10$

Answer:

Point-slope form: $y-4=-2(x-3)$ (or using the other point: $y-8=-2(x-1)$)
Slope-intercept form: $y=-2x+10$