Final answer:
The slope-intercept form of the line that passes through (-4,2) with slope m= 2.3 is y = 2.3x + 11.2, with the y-intercept being 11.2.
Step-by-step explanation:
To write the slope-intercept form of the line that passes through (-4,2) with slope m= 2.3, we use the slope-intercept equation y = mx + b, where m is the slope and b is the y-intercept. First, we'll substitute the known slope and the coordinates of the given point into the equation to find b.
Given point: (-4, 2)
Slope: m = 2.3
Substituting these values into the equation gives us:
2 = 2.3(-4) + b
2 = -9.2 + b
b = 2 + 9.2
b = 11.2
So, the slope-intercept form of the line is:
y = 2.3x + 11.2.
This equation shows that the y-intercept is 11.2, which means the line crosses the vertical (y) axis at the point (0, 11.2).