Questions: Write the slope-intercept form of the equation of the line through the given point with the given slope. 43) through: (-2,-4), slope = 1

Transcript text: Write the slope-intercept form of the equation of the line through the given point with the given slope. 43) through: $(-2,-4)$, slope $=1$

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 a point $(x_1, y_1)$ and the slope $ m $, we can substitute these values into the equation to solve for $ b $. Once $ b $ is found, we can write the full equation of the line.

Step 1: Identify the Given Information

We are given a point $(-2, -4)$ and a slope $m = 1$.

Step 2: Use the Slope-Intercept Form

The slope-intercept form of a line is given by the equation: \[ y = mx + b \] Substituting the known values, we have: \[ y = 1 \cdot x + b \]

Step 3: Solve for the Y-Intercept $b$

To find $b$, we substitute the coordinates of the given point $(-2, -4)$ into the equation: \[ -4 = 1 \cdot (-2) + b \] This simplifies to: \[ -4 = -2 + b \] Adding $2$ to both sides gives: \[ b = -2 \]

Step 4: Write the Final Equation

Now that we have both $m$ and $b$, we can write the equation of the line: \[ y = 1x - 2 \] or simply: \[ y = x - 2 \]