Questions: A line passes through the point (2,8) and has a slope of 9. Write an equation in slope-intercept form for this line.

Transcript text: A line passes through the point $(2,8)$ and has a slope of 9. Write an equation in slope-intercept form for this line. $\square$ $\square=\square$ $\square$

Solution

Solution Steps

To write the equation of a line in slope-intercept form (y = mx + b) given a point (x₁, y₁) and the slope (m), we can use the point-slope form of the equation of a line, which is y - y₁ = m(x - x₁). We then solve for y to convert it to slope-intercept form.

Solution Approach

Start with the point-slope form: y - y₁ = m(x - x₁).
Substitute the given point (2, 8) and the slope 9 into the equation.
Solve for y to get the equation in slope-intercept form.

Step 1: Identify the Given Information

We are given a point $(2, 8)$ and a slope $m = 9$. We need to find the equation of the line in slope-intercept form, which is expressed as $y = mx + b$.

Step 2: Use the Point-Slope Form

We start with the point-slope form of the equation of a line: \[ y - y_1 = m(x - x_1) \] Substituting the given values: \[ y - 8 = 9(x - 2) \]

Step 3: Simplify to Slope-Intercept Form

Now, we simplify the equation to solve for $y$: \[ y - 8 = 9x - 18 \] Adding 8 to both sides gives: \[ y = 9x - 10 \]