Slope and y-intercept

At every point on the y-axis, \(x=0\). Substituting \(x=0\) in \(y=7x+20\) gives \(y=7(0)+20=20\). Therefore, the line cuts the y-axis at \(y=20\). Here, \(7\) is the slope, not the y-intercept. Exam tip: in \(y=mx+c\), the y-intercept is \(c\).

A line in the form \(y=mx+c\) has slope \(m\). Here, the coefficient of \(x\) is \(-10\), so the slope is \(-10\) and its sign is negative. A zero slope occurs only when \(m=0\). Exam tip: In \(y=mx+c\), check the coefficient of \(x\) to identify the sign of the slope quickly.

A line in the form y = mx + c has slope m. Here, the coefficient of x is 14, so the slope is 14 and its sign is positive. A negative slope would require the coefficient of x to be less than 0. Exam tip: In y = mx + c, look at the coefficient of x to identify the sign of the slope quickly.

Using y = mx + b, identify the coefficient of x as the slope and the constant as the y-intercept. Here y = 0x - 7, so m = 0 and b = -7. The line therefore has no upward or downward tilt and crosses the y-axis at (0, -7). Option A is correct. Option B reverses the roles of the terms, whereas C and D incorrectly make the negative constant positive.

The equation is y = 21 − 8x, which can also be written as y = −8x + 21. The number multiplying x is −8, so the coefficient of x is −8. The term without x is 21, so it is the constant term. Option B misses the negative sign. Exam tip: a negative sign before a term is part of its coefficient.

At every point on the \(y\)-axis, \(x=0\). Substituting \(x=0\) in \(y=10-2x\) gives \(y=10\). Hence, the line cuts the \(y\)-axis at \((0,10)\). The point \((10,0)\) may relate to the \(x\)-intercept, but it is not on the \(y\)-axis. Exam tip: to find a \(y\)-intercept, always put \(x=0\).

A line parallel to the x-axis has slope 0, so its equation is \(y=c\). With y-intercept \(-4\), \(c=-4\), giving \(y=-4\). In contrast, \(x=-4\) is a vertical line. Exam tip: every equation of the form \(y=c\) is horizontal.

A line in the form y=mx+c has slope m, which gives the rate of change. Here, m=11, so an increase of 1 in x increases y by 11. The number 13 is the y-intercept, not the amount of increase. Exam tip: In y=mx+c, the coefficient of x is the slope.

The slope-intercept form of a line is \(y=mx+c\), where \(m\) is the slope. In \(y=\frac{4}{3}x-6\), the coefficient of \(x\) is \(\frac{4}{3}\), so the slope is \(\frac{4}{3}\). The value \(-6\) is the y-intercept, not the slope. Exam tip: In \(y=mx+c\), the coefficient of \(x\) is always the slope.

In the form \(y=mx+c\), \(c\) is the y-intercept. Here, \(c=5\), so the line crosses the y-axis at \((0,5)\), and its y-intercept is \(5\). \(-\frac{3}{8}\) is the slope, not the y-intercept. Exam tip: put \(x=0\) to find the y-intercept.

The slope-intercept form of a line is \(y=mx+c\), where \(m\) is the slope and \(c\) is the \(y\)-intercept. In \(y=3x+8\), \(m=3\) and \(c=8\), so option A is correct. Option B incorrectly interchanges the coefficient of \(x\) and the constant term. Exam tip: the coefficient of \(x\) gives the slope, while the constant term gives the \(y\)-intercept.

In \(y=mx+b\), \(m\) is the slope and \(b\) is the y-intercept. Parallel lines have equal slopes, so \(m=3\); with \(b=7\), the equation is \(y=3x+7\). Option A has the correct intercept but slope \(-3\). Exam tip: compare slope before intercept.

To find the slope, write the equation in the form \(y=mx+c\). Dividing \(2y=6x+10\) by 2 gives \(y=3x+5\). The coefficient of \(x\) is 3, so the slope is \(m=3\). Taking 6 as the slope is incorrect because it is the coefficient before making the coefficient of \(y\) equal to 1. Exam tip: after isolating \(y\), the coefficient of \(x\) is the slope.

To find the y-intercept, put x=0. Then 3y=9(0)-15=-15, so y=-5. Therefore, the line crosses the y-axis at -5. Taking -15 as the y-intercept is incorrect because it is the constant term before dividing the equation by 3. Exam tip: for the y-intercept, always substitute x=0.

The slope-intercept form is (y=mx+c), where (m) is the slope. The given equation can be written as (y=-2x+4), so the coefficient of (x) is -2 and the slope is -2. Although 2 is the magnitude, the negative sign shows that the line falls from left to right. Exam tip: In (y=mx+c), take the complete signed coefficient of (x) as the slope.

The line can be written in slope-intercept form as y=-3x+7. The y-intercept is the y-value when x=0. Substituting x=0 gives y=7, so the correct answer is 7. Here, -3 is the slope, not the y-intercept. Exam tip: In y=mx+c, c is the y-intercept.

The slope-intercept form of a line is \(y=mx+c\), where \(m\) is the slope and \(c\) is the \(y\)-intercept. Substituting \(m=6\) and \(c=-4\) gives \(y=6x-4\). In option B, the intercept has the wrong sign, because its \(y\)-intercept is \(+4\). Exam tip: put \(x=0\); the constant term gives the \(y\)-intercept.

The slope-intercept form of a straight-line equation is \(y=mx+b\). Here, \(m\) represents the slope and \(b\) represents the \(y\)-intercept. The question gives slope \(-4\), so the coefficient of \(x\) must be \(-4\). It also gives a \(y\)-intercept of 9, so the constant term must be 9. Substituting these two values into the standard form identifies the equation.

Using \(m=-4\) and \(b=9\), we obtain \(y=-4x+9\). This is option D. The equation \(y=4x+9\) has the correct intercept but the wrong slope because its slope is positive. The other choices either interchange the two numbers or change their signs, so they do not satisfy both given properties.

For every point on the y-axis, x=0. Substituting x=0 in y=5x+c gives y=c. The given y-intercept is (0,-3), so c=-3. If c were 3, the line would meet the y-axis at (0,3), not at the given point. Exam tip: in y=mx+c, c is directly the y-intercept.

In the form \(y=mx+c\), \(m\) represents the slope. Since the given slope is \(-7\), \(m=-7\). The number \(2\) is the y-intercept, not the slope. Exam tip: in \(y=mx+c\), the coefficient of \(x\) is always the slope.