Questions: A line passes through the point (-3,4) and has a slope of -5. Find an equation of this line. y=-5x-3 y=-3x-5 y=-5x-11 y=-3x+4

Transcript text: https://app.sophia.org/spcc/college-algebra-22-mi 1.= UNIT 3 - MILESTONE 3 Question 10 A line passes through the point $(-3,4)$ and has a slope of -5 . Find an equation of this line. $y=-5 x-3$ $y=-3 x-5$ $y=-5 x-11$ $y=-3 x+4$ SAVE \& CONTINUE Report an issue with this question

Solution

Solution Steps

To find the equation of a line given a point $(-3, 4)$ and a slope of $-5$, we can use the point-slope form of the equation of a line, which is $y - y_1 = m(x - x_1)$. Here, $(x_1, y_1)$ is the given point and $m$ is the slope. We will then simplify this equation to the slope-intercept form $y = mx + b$.

Step 1: Identify the Given Information

We are given a point $(-3, 4)$ and a slope $m = -5$.

Step 2: Use the Point-Slope Form

We will use the point-slope form of the equation of a line, which is given by: \[ y - y_1 = m(x - x_1) \] Substituting the values: \[ y - 4 = -5(x + 3) \]

Step 3: Simplify to Slope-Intercept Form

Expanding and simplifying the equation: \[ y - 4 = -5x - 15 \] Adding $4$ to both sides: \[ y = -5x - 11 \]