a line passes through the points (-1, 10) and (4, -10). write its equation in slope-intercept form. write…

Explanation:

Step1: Calculate the slope

The slope ( m ) between two points ((x_1, y_1)) and ((x_2, y_2)) is given by the formula ( m=\frac{y_2 - y_1}{x_2 - x_1} ). Here, ( x_1=-1,y_1 = 10,x_2 = 4,y_2=-10 ). So ( m=\frac{- 10-10}{4-\left(-1\right)}=\frac{-20}{5}=-4 ).

Step2: Find the y - intercept

We use the slope - intercept form ( y=mx + b ). We know ( m=-4 ) and we can use one of the points, say ((-1,10)). Substitute ( x=-1,y = 10 ) and ( m=-4 ) into ( y=mx + b ): ( 10=-4\times(-1)+b ). Simplify the right - hand side: ( 10 = 4 + b ). Subtract 4 from both sides: ( b=10 - 4=6 ).

Step3: Write the equation

The slope - intercept form is ( y=mx + b ). Substitute ( m=-4 ) and ( b = 6 ) into the formula, we get ( y=-4x+6 ).

Answer:

( y=-4x + 6 )