Let's break down this problem:

a.) Write an equation of a line with the slope $m = 4$, which passes through the point $(1, -1)$.

We'll use the point-slope form equation for this part. The point-slope form of a line is given by:

$y - y_1 = m(x - x_1)$

Where:

• $m$ is the slope,
• $(x_1, y_1)$ is a point on the line.

Given $m = 4$ and the point $(1, -1)$, substitute into the formula:

$y - (-1) = 4(x - 1)$

Simplifying:

$y + 1 = 4(x - 1)$

This is the equation in point-slope form.

b.) Write the equation in slope-intercept form $y = mx + b$.

To convert the equation to slope-intercept form, we'll solve for $y$:

$y + 1 = 4(x - 1)$

Distribute the 4:

$y + 1 = 4x - 4$

Subtract 1 from both sides:

$y = 4x - 5$

So the equation in slope-intercept form is:

$y = 4x - 5$

Summary:

• Point-slope form: $y + 1 = 4(x - 1)$
• Slope-intercept form: $y = 4x - 5$

Would you like help with graphing this equation?

Relative Questions:

1. What is the formula for the slope of a line given two points?
2. How can you determine if two lines are parallel or perpendicular based on their slopes?
3. How do you convert a standard form linear equation into slope-intercept form?
4. How does the graph of a linear equation change when the slope increases or decreases?
5. What does the y-intercept of a line tell you about its graph?

Tip: To graph a line easily, identify the slope (rise over run) and y-intercept first. This gives you a starting point and direction to plot!