Question

7-9. write the equation of the line with x-intercept (-4, 0) and y-intercept (0, 9). homework help

Explanation:

Step1: Recall the intercept form of a line

The intercept form of a line is given by $\frac{x}{a}+\frac{y}{b} = 1$, where $a$ is the $x$-intercept and $b$ is the $y$-intercept.
Here, the $x$-intercept $a=- 4$ and the $y$-intercept $b = 9$.

Step2: Substitute the values of $a$ and $b$ into the intercept form

Substituting $a=-4$ and $b = 9$ into $\frac{x}{a}+\frac{y}{b}=1$, we get:
$\frac{x}{-4}+\frac{y}{9}=1$

Step3: Convert to slope - intercept form (optional, but to get a more familiar form)

First, simplify $\frac{x}{-4}+\frac{y}{9}=1$.
Multiply through by 36 (the least common multiple of 4 and 9) to clear the fractions:
$36\times\frac{x}{-4}+36\times\frac{y}{9}=36\times1$
$- 9x + 4y=36$
Then, solve for $y$:
$4y=9x + 36$
$y=\frac{9}{4}x + 9$

We can also use the two - point form. The two points are $(-4,0)$ and $(0,9)$.

Step1 (Alternative: Using two - point form)

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$
Here, $x_1=-4,y_1 = 0,x_2=0,y_2=9$
So, $m=\frac{9 - 0}{0-(-4)}=\frac{9}{4}$

Step2 (Alternative: Using slope - intercept form $y=mx + b$)

We know that the $y$-intercept $b = 9$ (from the point $(0,9)$) and the slope $m=\frac{9}{4}$
So the equation of the line is $y=\frac{9}{4}x+9$ (which is the same as we got earlier from the intercept form conversion)

Answer:

The equation of the line is $y=\frac{9}{4}x + 9$ (or in intercept form $\frac{x}{-4}+\frac{y}{9}=1$)