Final answer:
To find the y-intercept value of g where the line crosses the y-axis, calculate the slope using the points where the line crosses the x-axis (-2, 0) and another known point (5, 3). The y-intercept g is the same as the y-coordinate of the known point, which is 3.
Step-by-step explanation:
The graph of a line crosses the x-axis at x-coordinate -2 and passes through the point (5,3). To find the value of g, where the line crosses the y-axis, we need to calculate the line's slope and use it to find the y-intercept. First, the slope of the line (m) can be calculated by using the two given points, (-2,0) and (5,3).
The slope m is given by the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the values, we get:
m = (3 - 0) / (5 - (-2)) = 3 / 7
Now, using the slope-point form of a line's equation, where y - y1 = m(x - x1), and choosing the point (5,3), we have:
3 - 3 = (3/7)(5 - 5)
Thus, the equation of the line in slope-intercept form (y = mx + b) is:
y = (3/7)x + 3
To find the y-intercept g, we set x = 0:
g = (3/7)(0) + 3 = 3
Therefore, the y-intercept of the line is 3, and that means g = 3.