Choose the slope-intercept equation of the line that passes through the point shown (with graph)?

D. the slope cannot be negative with that graph

The regular convention for a straight line graph is y = mx + c, the place m is the gradient. This also signifies that the coefficient of x is the gradient The gradient is a evaluation between features so solving this equation for m (i cannot do it right here, with ease consider me...:-)) m = (y1 - y2) divided by way of utilizing (x1 - x2) => m = (four - -6) divided by way of (-1 -4) => m = 10 divided by means of -5 => m = -2 because of this that your line will appear like a again scale down, as the gradient is slash than zero (ii) the long-established expression for a straight line is y = mx + c but we've got bought cleverly decided that m = -2 (from above) So, y = -2x + c We even have coordinates for two elements; let's remember the fundamental one (-1,four) we all know on this case that y = four, and x = -1 for this reason, substituting the phrases that everyone knows, will support us resolve for c 4 = (-2 x -1) + c => four = 2 + c => 4-2 = c for that reason c = 2 hence the equation( y = mx +c) is y = -2x + 2 (iii) the x intercept is the factor where y = 0 for that reason, headquartered on our equation above zero = -2x + 2 => 2x = 2 => x = 1 Intercept is a (1,zero) (iv) For (2,-2) to be on the street, requires that we satisfy the equation for the avenue y = -2x + 2 If x = 2, then y = (-2 increased via 2) + 2 => y = -four + 2 => y = -2 So, if x = 2, y have got to equal -2 to lie on the avenue. This component (2,-2) satisfies the equation for the straight line, so (2,-2) is a factor on the line (v) : 1) that the x intercept happens at (1,zero) 2) the gradient is -2 To be parallel, the new line have acquired to have the same gradient. Lets make x = 2 ( for illustration; you could additionally decide upon any fee for x) for that reason, the x intercept for the company new line would be at (2,zero), as y would = zero at this factor (as above) y = mx + c => 0 = (-2 x 2) + c => four = c as a consequence, a line parallel to y = -2x + 2 is y = -2x + 4 good good fortune!