Question

How do you find the slope and intercept of the graph of $ 4x + 3y - 7 = 0 $ ?

Answer 1

Hint: We know the equation of a line passing through a point and having a slope ‘m’ and with ‘y’ intercept as ‘c’ is given by $ y = mx + c $ . Here, (x, y) is a variable. We convert the given equation to the slope intercept form. Then comparing the simplified equation with the equation of slope intercept we will get the desired result.

Complete step-by-step answer:
In the given problem, we are required to find the slope and intercept of the line whose equation is given to us as $ 4x + 3y - 7 = 0 $ .
The slope intercept form of the equation of a line is $ y = mx + c $ where slope of line is given by ‘m’ and y-intercept is given by ‘c’.
So, $ 4x + 3y - 7 = 0 $
Shifting term consisting y to right side of the equation,
 $ \Rightarrow 4x + 3y - 7 = 0 $
 $ \Rightarrow 3y = 7 - 4x $
Isolating y so as to convert the equation of line to slope and intercept form, we get,
 $ \Rightarrow y = \left( {\dfrac{{7 - 4x}}{3}} \right) $
Now, we can directly start comparing the equation of the given line with the slope and intercept form of a line and get the values of slope and intercept of the line.
Therefore, On comparing the equation of the line $ y = - \dfrac{4}{3}x + \dfrac{7}{3} $ given to us and the slope intercept form of the line $ y = mx + c $ , we get,
Slope of the line $ = m = - \dfrac{4}{3} $ and y-intercept $ = c = \dfrac{7}{3} $ .
So, the correct answer is “$ = m = - \dfrac{4}{3} $ and y-intercept $ = c = \dfrac{7}{3} $”.

Note: ‘y’ intercept is defined as a line or a curve crosses the y-axis of a graph. In other words the value of ‘y’ at ‘x’ is equal to zero. Hence, the y intercept of a line can also be found by putting the value of x as zero. Slope of a line is the inclination of the straight line with positive x-axis.