The graph of linear function `g` passes through the points `\left(-5,-1\right)`and `\left(5,\ 5\right),`as shown. What are the slope and y-intercept of the graph `g`?
To find the slope of the graph `g`, we use the formula for slope:
m = (y2 - y1) / (x2 - x1)
Using the points given:
m = (5 - (-1)) / (5 - (-5))
m = 6 / 10
m = 0.6
Therefore, the slope of the graph `g` is 0.6.
To find the y-intercept of the graph `g`, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Using one of the given points, say (-5, -1), and the slope we found (0.6):
y - (-1) = 0.6(x - (-5))
y + 1 = 0.6(x + 5)
y + 1 = 0.6x + 3
y = 0.6x + 2
Therefore, the y-intercept of the graph `g` is 2.