A line has a slope of -2 and a y-intercept of -7. Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest... A line has a slope of -2 and a y-intercept of -7. Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.
Understand the Problem
The question is asking for the equation of a line in slope-intercept form (y = mx + b) using the provided slope and y-intercept. The slope is -2, and the y-intercept is -7, so we need to substitute these values into the equation.
Answer
$y = -2x - 7$
Answer for screen readers
The equation of the line is $y = -2x - 7$.
Steps to Solve
- Identify the slope and the y-intercept
From the problem, the slope ($m$) is given as $-2$, and the y-intercept ($b$) is $-7$.
- Substitute into the slope-intercept form
The slope-intercept form of a line is given by the equation $y = mx + b$.
Now, substituting the values of $m$ and $b$:
$$ y = -2x - 7 $$
This is the equation of the line in slope-intercept form.
The equation of the line is $y = -2x - 7$.
More Information
In the slope-intercept form, $y = mx + b$, $m$ represents the slope of the line, which indicates the steepness and direction, while $b$ represents the y-intercept, which is the point where the line crosses the y-axis. This means for every unit increase in $x$, $y$ decreases by 2 units, and the line starts at -7 on the y-axis.
Tips
- A common mistake is to misplace the signs when substituting the slope or the y-intercept. It's important to carefully check the values given in the problem to ensure they are substituted correctly.
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