Question

How do you find the y-intercept of \[ - 8x + 6y = 42\]?

Answer 1

Hint: The point where the line or curve crosses the axis of the graph is called intercept. If a point crosses the y-axis, then it is called y-intercept. As the given equation consists of both x and y variables hence, to find the y-intercept of the given equation, we just need to substitute \[x\]= 0 in the given equation and solve for y.

Complete step-by-step solution:
The given equation is
\[\Rightarrow - 8x + 6y = 42\]
As we need to find the y-intercept, substitute \[x\]= 0 in the given equation and solve for y i.e.,
\[\Rightarrow - 8\left( 0 \right) + 6y = 42\]
After simplifying we get
\[\Rightarrow 6y = 42\]
Divide both sides by 6 to get the value of y as
\[\Rightarrow \dfrac{{6y}}{6} = \dfrac{{42}}{6}\]
\[\Rightarrow y = \dfrac{{42}}{6}\]
Therefore, the value of y is
\[\Rightarrow y = 7\]
Hence, the y-intercept of \[ - 8x + 6y = 42\] is \[\left( {0,7} \right)\].

Additional information:
-If a point crosses the x-axis, then it is called x-intercept. If a point crosses the y-axis, then it is called y-intercept. If the axis is not specified, usually the y-axis is considered. It is y-coordinate of a point where a straight line or a curve intersects the y-axis.
-Slope intercept form is the general form of straight-line equation. It is represented as:
\[y = mx + c\]
Here, c is the y-intercept and m is the slope, hence it is called a slope-intercept form.
-Straight line equation gives the graph of a straight line. They are also called linear equations and consist of simple variables. As we can see in the expression, \[y = mx + c\], x and y are the variables, where x is an independent variable and y is a dependent variable. If we put the values of x, then we can get the respective values of y and then we plot the graph.

Note: As per the given equation consists of x and y terms based on the intercept asked, we need to solve for it. For ex if y-intercept is asked substitute x=0 and solve for y and if x-intercept is asked substitute y=0 and solve for x and the y-intercept of an equation is a point where the graph of the equation intersects the y-axis.