find the intercepts of the line that contains each pair of points (-1,-4) (6,10)

For the linear equation that contains the points (-1,-4) and (6,10), we have that:The y-intercept is y = -2.The x-intercept is x = 1.What is a linear function?A linear function is modeled by:[tex]y = mx + b[/tex]In which:m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.In this problem, it has points (-1,-4) and (6,10), hence, considering the slope is given by change in y divided by change in x, we have that:[tex]m = \frac{10 - (-4)}{6 - (-1)} = 2[/tex]Then:[tex]y = 2x + b[/tex]Point (6,10) means that when x = 6, y = 10, and this is used to find b.[tex]y = 2x + b[/tex][tex]10 = 2(6) + b[/tex][tex]b = -2[/tex]The function is:[tex]y = 2x - 2[/tex]The y-intercept is y = -2.For the x-intercept, we have that:[tex]2x - 2 = 0[/tex][tex]x = 1[/tex]The x-intercept is x = 1.You can learn more about linear equations at