Question

1. slope (m) =

y-intercept (b) =
equation:
graph of a line on a coordinate plane with x-axis from -5 to 5 and y-axis from -5 to 5, passing through points like (-5, -4), (-3, -2), (0, 1), (3, 4)

Explanation:

Step1: Find the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points on the line, for example, $(0, 1)$ (the y - intercept) and $(3, 4)$. Then $m=\frac{4 - 1}{3 - 0}=\frac{3}{3}=1$.

Step2: Find the y - intercept (b)

The y - intercept is the point where the line crosses the y - axis. From the graph, the line crosses the y - axis at $(0, 1)$, so $b = 1$.

Step3: Write the equation

The slope - intercept form of a line is $y=mx + b$. Substituting $m = 1$ and $b = 1$ into the formula, we get $y=x + 1$.

Answer:

slope (m) = $1$; y - intercept (b) = $1$; equation: $y=x + 1$