Question

How do you find the slope of the line \[y = - 8x + 4\]?

Answer 1

Hint: First, we will figure out what type of formula should be used. Here, we know that the line is in the form of slope-intercept form. Every equation that is in this form has a slope ‘m’. So, after that we will find the slope from the help of the slope-intercept form.

Complete step by step solution:
To find the slope, first we have to convert the equation in a slope-intercept form. The slope-intercept form is:
\[y = mx + c\]
We can see that the question is already in the slope-intercept form. So, to find the slope, we just have to identify the term from the slope-intercept form which is known as the slope.
Here, from this slope-intercept form we get that the coefficient of ‘x’ is ‘m’ and m= slope. Here, c= y-intercept.
According to the slope-intercept formula, we get that:
\[m = - 8\] and \[c = 4\]

Therefore, we get that the slope of the line \[y = - 8x + 4\] is \[ - 8\].

Additional information:
Slope in Mathematics means the ratio of rate of change of values of x and values of y. If we write the formula of slope, then we write it as \[{\text{slope = }}\dfrac{{{\text{rate}}\,{\text{of}}\,{\text{change}}\,{\text{in}}\,{\text{values}}\,{\text{of}}\,{\text{y}}}}{{{\text{rate}}\,{\text{of}}\,{\text{change}}\,{\text{in}}\,{\text{values}}\,{\text{of}}\,{\text{x}}}}\]. The formula can be written as \[m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\]. Slope is also represented as \[{\text{slope = }}\dfrac{{{\text{rise}}}}{{{\text{run}}}}\]. Slope is expressed as rise over run.

Note: Slope is actually the steepness of a line. If a line is aligned or positioned from the bottom left to upper right, then the slope is a positive slope. If a line is aligned from upper left to bottom right, then the slope is a negative slope.