Write an equation in slope-intercept form for the line with slope -7 and $y$-intercept 7.
Answer (2)
The slope-intercept form of a linear equation is y = m x + b , where m is the slope and b is the y-intercept.
Substitute the given slope m = − 7 and y-intercept b = 7 into the slope-intercept form.
The equation becomes y = − 7 x + 7 .
The equation of the line in slope-intercept form is y = − 7 x + 7 .
Explanation
Understanding the Problem We are given the slope and y -intercept of a line, and we need to write the equation of the line in slope-intercept form.
Recalling Slope-Intercept Form The slope-intercept form of a linear equation is given by y = m x + b , where m is the slope and b is the y -intercept.
Substituting Values We are given that the slope m = − 7 and the y -intercept b = 7 . Substituting these values into the slope-intercept form, we get y = ( − 7 ) x + 7 .
Writing the Equation Therefore, the equation of the line in slope-intercept form is y = − 7 x + 7 .
Examples
Understanding linear equations is crucial in many real-world scenarios. For instance, if you're tracking the depreciation of a car's value over time, you can use a linear equation. Suppose a car initially costs $20,000 and depreciates by 2 , 000 e a c h ye a r . T h ec a r ′ s v a l u e , y , a f t er x ye a rsc anb e m o d e l e d a s y = -2000x + 20000$. This equation helps predict the car's value at any point in time, aiding in financial planning or resale decisions.
The equation of the line in slope-intercept form is y = − 7 x + 7 , where -7 is the slope and 7 is the y-intercept. This indicates that the line decreases in value as x increases. Each unit increase in x results in a decrease of 7 units in y .
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