We are given a graph of a line and are asked to find the following: (a) The y-intercept of the line. (b) The slope of the line. (c) The equation of the line in standard form.

1. Problem Description

We are given a graph of a line and are asked to find the following:

(a) The y-intercept of the line.

(b) The slope of the line.

(c) The equation of the line in standard form.

2. Solution Steps

(a) The y-intercept is the point where the line crosses the y-axis. From the graph, we can see the line intersects the y-axis at approximately $y = -1$.

(b) To find the slope of the line, we need two points on the line. We are given the point $(-5, 3)$. From the graph, it appears that the line also passes through the point $(0, -1)$. The slope, $m$, is given by the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Using the points $(-5, 3)$ and $(0, -1)$, we have:

$m = \frac{-1 - 3}{0 - (-5)} = \frac{-4}{5} = -\frac{4}{5}$

(c) Now we need to find the equation of the line in standard form, which is $Ax + By = C$, where $A, B,$ and $C$ are integers, and $A$ is positive. We can use the slope-intercept form of a line:

$y = mx + b$

where $m$ is the slope and $b$ is the y-intercept. We already found that $m = -\frac{4}{5}$ and $b = -1$. Thus, the equation is:

$y = -\frac{4}{5}x - 1$

To convert this to standard form, we want to eliminate the fraction. Multiply both sides of the equation by $5$:

$5y = -4x - 5$

Now, move the $x$ term to the left side:

$4x + 5y = -5$

3. Final Answer

(a) The y-intercept is -

1. (b) The slope is $-\frac{4}{5}$.

(c) The equation of the line in standard form is $4x + 5y = -5$.