Questions: A line passes through the point (-1,2) and has a slope of 8. Write an equation in slope-intercept form for this line.

Transcript text: A line passes through the point $(-1,2)$ and has a slope of 8 . Write an equation in slope-intercept form for this line.

Solution

Solution Steps

To find the equation of a line in slope-intercept form, which is $ y = mx + b $, we need the slope $ m $ and the y-intercept $ b $. We are given the slope $ m = 8 $ and a point on the line $(-1, 2)$. We can substitute these values into the slope-intercept equation to solve for $ b $.

Step 1: Identify the Given Information

We are given a point on the line $(-1, 2)$ and the slope $m = 8$.

Step 2: Use the Slope-Intercept Form

The slope-intercept form of a line is given by the equation: \[ y = mx + b \] where $m$ is the slope and $b$ is the y-intercept.

Step 3: Substitute the Known Values

Substituting the known values into the equation to find $b$: \[ 2 = 8(-1) + b \] This simplifies to: \[ 2 = -8 + b \]

Step 4: Solve for the Y-Intercept

Rearranging the equation to solve for $b$: \[ b = 2 + 8 = 10 \]

Step 5: Write the Final Equation

Now that we have both $m$ and $b$, we can write the equation of the line: \[ y = 8x + 10 \]