Question

write the slope-intercept form of the equation of the line described.

1. through: $(-1,-1)$, parallel to $y=3x-2$
2. through: $(-1,3)$, parallel to $y=2x-4$

Explanation:

Problem 5:

Step1: Identify parallel slope

Parallel lines have equal slopes. For $y=3x-2$, slope $m=3$.

Step2: Use point-slope formula

Point-slope form: $y-y_1=m(x-x_1)$. Substitute $m=3$, $(x_1,y_1)=(-1,-1)$:
$y-(-1)=3(x-(-1))$

Step3: Simplify to slope-intercept form

Simplify and solve for $y$:
$y+1=3(x+1)$
$y+1=3x+3$
$y=3x+3-1$
$y=3x+2$

Problem 6:

Step1: Identify parallel slope

Parallel lines have equal slopes. For $y=2x-4$, slope $m=2$.

Step2: Use point-slope formula

Point-slope form: $y-y_1=m(x-x_1)$. Substitute $m=2$, $(x_1,y_1)=(-1,3)$:
$y-3=2(x-(-1))$

Step3: Simplify to slope-intercept form

Simplify and solve for $y$:
$y-3=2(x+1)$
$y-3=2x+2$
$y=2x+2+3$
$y=2x+5$

Answer:

1. $y=3x+2$
2. $y=2x+5$