Question

find the slope - intercept equation of the line that passes through (-1,-4) and has a slope of 2. show your work here enter your answer find the slope - intercept equation of the line that passes through (3,1) and has a slope of -\frac{1}{2}. show your work here enter your answer

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Substitute values for first line

For the line passing through $(-1,-4)$ with slope $m = 2$, substitute $x=-1$, $y = - 4$, and $m = 2$ into $y=mx + b$. We get $-4=2\times(-1)+b$.

Step3: Solve for $b$ for first line

Simplify the equation: $-4=-2 + b$. Add 2 to both sides, $b=-4 + 2=-2$. So the equation is $y = 2x-2$.

Step4: Substitute values for second line

For the line passing through $(3,1)$ with slope $m=-\frac{1}{2}$, substitute $x = 3$, $y = 1$, and $m=-\frac{1}{2}$ into $y=mx + b$. We get $1=-\frac{1}{2}\times3 + b$.

Step5: Solve for $b$ for second line

Simplify the equation: $1=-\frac{3}{2}+b$. Add $\frac{3}{2}$ to both sides. $b=1+\frac{3}{2}=\frac{2 + 3}{2}=\frac{5}{2}$. So the equation is $y=-\frac{1}{2}x+\frac{5}{2}$.

Answer:

$y = 2x-2$
$y=-\frac{1}{2}x+\frac{5}{2}$