Questions: Find the slope-intercept form of the equation of the line with the given properties. Slope = 2; containing the point (-3,-4) A. y = -2x + 2 B. y = 2x + 2 C. y = 2x - 2 D. y = -2x - 2

Find the slope-intercept form of the equation of the line with the given properties. Slope = 2; containing the point (-3,-4) A. y = -2x + 2 B. y = 2x + 2 C. y = 2x - 2 D. y = -2x - 2

Transcript text: Fall 2024 Find the slope-intercept form of the equation of the line with the given properties. Slope $=2$; containing the point $(-3,-4)$ A. $y=-2 x+2$ B. $y=2 x+2$ C. $y=2 x-2$ D. $y=-2 x-2$

Solution

Solution Steps

To find the slope-intercept form of the equation of a line, we use the formula $ y = mx + b $, where $ m $ is the slope and $ b $ is the y-intercept. Given the slope $ m = 2 $ and a point $(-3, -4)$ on the line, we can substitute these values into the equation to solve for $ b $.

Step 1: Identify the Slope and Point

We are given the slope $ m = 2 $ and a point on the line $ (-3, -4) $.

Step 2: Use the Point-Slope Formula

The slope-intercept form of a line is given by the equation: \[ y = mx + b \] Substituting the known values into the equation, we have: \[ -4 = 2(-3) + b \]

Step 3: Solve for the Y-Intercept

Now, we can solve for $ b $: \[ -4 = -6 + b \implies b = -4 + 6 = 2 \]

Step 4: Write the Equation

Now that we have both $ m $ and $ b $, we can write the equation of the line: \[ y = 2x + 2 \]