Q:

please help, show all work, asapppFind the slope through the points (12, -18), (11,12)Find the slope through the points (-18, -20), (-18, -15)Find the X and Y intercepts: 4x + y = 5Find the X and Y intercepts: y = 5x - 4Write the equation of the line with a slope of zero and the point (3,4)?What is the slope of the line x = 1?

Accepted Solution

A:
QUESTION 1We want to find the slope through the points (12,-18), (11,12).We use the slope formula,[tex]m = \frac{y_2-y_1} {x _2-x_1} [/tex]We substitute the points to get,[tex]m = \frac{12 - - 18}{11 - 12} [/tex][tex]m = \frac{30}{ - 1} = - 30[/tex]The slope is -30.QUESTION 2.We want to find the slope through the points (-18, -20), (-18, -15).We use the slope formula again to obtain,[tex]m = \frac{ - 15 - - 20}{ - 18 - - 18} [/tex]We simplify to get;[tex]m = \frac{5}{0} [/tex]Division by zero means the slope is not defined.QUESTION 3The given equation is 4x + y = 5.At x-intercept, y=0.We put y=0 into the equation to get,[tex]4x + 0 = 5[/tex][tex]4x = 5[/tex][tex]x = \frac{5}{4} [/tex]The x-intercept is [tex]( \frac{5}{4} , 0)[/tex]To find the y-intercept,we substitute x=0 into the equation to get,[tex]4(0) + y = 5[/tex][tex]y = 5[/tex]The y-intercept is (0,5)QUESTION 4.The given equation is [tex]y = 5x - 4[/tex]To find the y-intercept put x=0 into the equation.[tex]y = 5(0) - 4[/tex][tex]y = - 4[/tex](0,-4)To find the x-intercept, put y=0,[tex]0 = 5x - 4[/tex][tex]4 = 5x[/tex][tex] \frac{4}{5} = x[/tex][tex]( \frac{4}{5} ,0)[/tex]QUESTION 5To find the equation of a line given the slope m, and a point [tex](x_1,y_1) [/tex]we use the formula,[tex]y-y_1=m(x-x_1)[/tex]The given line has slope zero and passes through (3,4)The equation is[tex]y - 4 = 0(x - 3)[/tex][tex]y - 4 = 0[/tex][tex]y = 4[/tex]Question 6The given equation is [tex]x = 1[/tex]This is the equation of a line that is parallel to the y-axis.The slope of all lines parallel to the x-axis is undefined.The slope of x=1 is not defined.