Questions: The equation of a line is given below. 4x+6y=-36 Find the x-intercept and the y-intercept. Then use them to graph the line. x-intercept: y-intercept:

The equation of a line is given below.
4x+6y=-36

Find the x-intercept and the y-intercept.
Then use them to graph the line.
x-intercept:
y-intercept:

Transcript text: The equation of a line is given below. \[ 4 x+6 y=-36 \] Find the $x$-intercept and the $y$-intercept. Then use them to graph the line. $x$-intercept: $\square$ $\square$ $\square$ $\square$ $y$-intercept: $\square$

Solution

Solution Steps

Step 1: Finding the $x$-intercept

To find the $x$-intercept, we set $y = 0$ in the equation $ax + by = c$. Solving for $x$, we get $x = \frac{c}{a} = \frac{-36}{4}$. Thus, the $x$-intercept is -9.

Step 2: Finding the $y$-intercept

To find the $y$-intercept, we set $x = 0$ in the equation $ax + by = c$. Solving for $y$, we get $y = \frac{c}{b} = \frac{-36}{6}$. Thus, the $y$-intercept is -6.

Step 3: Finding the slope

The slope $m$ of the line can be found by rearranging the equation into slope-intercept form $y = mx + b$, where $m = -\frac{a}{b} = -\frac{4}{6}$. Thus, the slope is -0.67.

Final Answer:

The line described by the equation $4x + 6y = -36$ has an $x$-intercept of -9, a $y$-intercept of -6, and a slope of -0.67. To graph this line, plot the points at the $x$-intercept and $y$-intercept on the Cartesian plane and draw a straight line through them. Alternatively, start at the $y$-intercept on the y-axis and use the slope to find another point on the line.

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