Which linear function represents the line given by the point-slope equation y + 7 = –2/3(x + 6)? f(x) = –2/3x – 11f(x) = –2/3x – 1f(x) = –2/3x + 3 f(x) = –2/3x + 13

Answer: First option: [tex]f(x)=-\frac{2}{3}x-11[/tex] Step-by-step explanation: Given the point-slope equation [tex]y+7=-\frac{2}{3}(x+6)[/tex], you need to solve for [tex]y[/tex], because you are looking for the equation of the line in slope-intercept form: [tex]y=mx+b[/tex] Being [tex]m[/tex] the slope of that line, and [tex]b[/tex] the intersection of the line with the y-axis. Then: Apply Distributive property: [tex]y+7=-\frac{2}{3}x-4[/tex] Subtract 7 from both sides: [tex]y+7-(7)=-\frac{2}{3}x-4-(7)\\y=-\frac{2}{3}x-11[/tex] Rewrite the equation: [tex]f(x)=-\frac{2}{3}x-11[/tex] (The linear function of the First option)