Final answer:
To write the equation in slope-intercept form, we need to find the slope and the y-intercept. Using the coordinates (-4, -6) and (0, 10), we can calculate the slope as 4. Plugging the slope and one of the points into the point-slope form, the equation is y = 4x + 10.
Step-by-step explanation:
To write the equation in slope-intercept form, we need to find the slope and the y-intercept. The slope, m, can be found using the formula: m = (y2 - y1)/(x2 - x1). Let's use the coordinates (-4, -6) and (0, 10) to find the slope:
m = (10 - (-6))/(0 - (-4))
m = 16/4 = 4
Now, we can use the point-slope form: y - y1 = m(x - x1). Let's use (-4, -6) as our point:
y - (-6) = 4(x - (-4))
y + 6 = 4(x + 4)
Next, simplify the equation:
y + 6 = 4x + 16 (Distribute 4 to both x and 4)
y = 4x + 16 - 6 (Subtract 6 from both sides)
y = 4x + 10
Therefore, the equation of the line passing through (-4, -6) and (0, 10) in slope-intercept form is y = 4x + 10.
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