Equations of lines Find an equation of the lines with the following properties. Graph the lines. a. The line passing through the points (2, ?3) and (4, 2) b. The line with slope ? and x? -intercept (?4, 0) c. The line with intercepts (4, 0) and (0, ?2)

Step-by-step solution Step 1 a) We need to find the equation of the line passing through the points (2, -3) and (4, 2). Step 2 To solve the problem, we use the Point-Slope Form of the equating of a line yy =1m(xx ) [1]1 with slope = m = y21 [2] x21 Step 3 Substituting [2] into [1], we get: yy = ( y21)(xx ) [3] 1 x21 1 Step 4 Using the given points (2, -3) and (4, 2) and [3] to find the equation of the line, we get: 2(3) y(3) = ( 42 )(x2) [4] Step 5 Simplifying and rearranging [4] i nto lope-Intercept Form, we get: y+3 = (x2) 2 y = x8 2 Step 6 Therefore, the equation for the line passing through the points (2, -3) and (4, 2) is: 5 y = x28 The graph of the function is shown below: Step 7 3 b) We need to find the equation of the line with slope 4 and x-intercept (-4, 0). Step 8 To solve the problem, we use the P oint-Slope Form of the equating of a line. yy = 1(xx ) [5] 1 Step 9 3 Using the given slope , x4intercept (-4, 0) and [5] to find the equation of the line, we get: y(0) = (x(4)) [6] 4